Thanks to the directional reflection supported by \(R\)  riss, as shown in Fig. REF , the channel between each bs and each user in the proposed RIS-aided cell-free network consists of two parts: the BS-user link and \(R\)  BS-RIS-user links, where each BS-RIS-user link can be further divided into a BS-RIS link and a RIS-user link. The signal reflection on the riss can be modeled by multiplying the incident signal with a phase shift matrix and forwarding the phase shifted signal to the user [1]}. Therefore, the equivalent channel \({{\bf {h}}_{b,k,p}^H}\)  from the \(b\) -th bs to the \(k\) -th user on the \(p\) -th subcarrier can be written as [2]}
\({{\bf {h}}_{b,k,p}^H} = \underbrace{{{\bf {H}}_{b,k,p}^H}}_{\text{BS-user link}} + \underbrace{\sum \limits _{r = 1}^R {{{\bf {F}}_{r,k,p}^H{\bf {\Theta }}_r^H{{\bf {G}}_{b,r,p}}}} }_{\text{BS-RIS-user links}},\) 
